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SummaryTo reduce fuel oil costs and emission of greenhouse gases of ships in operation, application of Contra-Rotating Propellers (CRP) will be one of the solutions, which have high propulsive efficiency. Although several estimation methods of predicting open water characteristics of CRP have been developed in the past, few methods treat accurately with trailing wake geometry, which influences much on estimate accuracy. CRP makes the flow around the propellers more complicated compared with conventional single propeller because aft and forward propeller of CRP interacts each other strongly. In order to improve estimate accuracy, more rigorous treatment of the trailing wake geometry is desirable.This paper presents a calculation method, taking deformation of trailing wake accurately into account. The method is based on a simplified surface panel method "SQCM" which satisfies the Kutta condition easily. The SQCM consists of Hess and Smith type source panels on the propeller surface and discrete vortices on the camber surface according to Lan's QCM (Quasi-Continuous vortex lattice Method). The wake vortex lines are arranged in accordance with the direction of the flow including induced velocity by both propellers. We show some calculated results and validate them by comparing experiments in this paper. It is found that thrust and torque of the aft propeller differ considerably depending on which the deformation of trailing wake is taken into account or not. The calculated results with deformed wake agrees very well with the experiment, while the calculated results without deformed wake always overestimate the thrust and torque of the aft propeller.

This paper presents a calculation method for the unsteady cavitating propeller problem. The method is based on a simplified surface panel method "SQCM" which satisfies the Kutta condition easily. Hess and Smith type source panels are distributed on the propeller and cavity surface. Discrete vortices are distributed on the camber surface according to Lan's QCM (Quasi-Continuous vortex lattice Method). The boundary conditions to determine these singularities are the constant pressure condition on the cavity surface and the zero normal velocity condition on the propeller and camber surface. In the unsteady problem, we give the modified normal velocity instead of zero normal velocity at the end of camber surface in order to satisfy the Kutta condition exactly. The cavity shape in each radial section is determined so that the zero normal velocity condition is satisfied. In the present method, a cavity length for each radial section is given first. Then the singularities and the cavity shapes are determined. These steps are repeated until both constant pressure condition and normal velocity condition are satisfied on the cavity surface. Next, the cavity length is corrected in order that the opening at the cavity end will get closer to the target value. By using the corrected cavity length, the calculation is repeated from the beginning. These steps are repeated until the opening at the cavity end agrees with the target value in each section. In this method, constant pressure condition is satisfied including cross flow velocity because its effect is not small near the tip of a propeller blade. The variation of cavitation patterns, cavity shapes, cavity area and cavity volume in wake are calculated for two kinds of propellers. Good agreements are obtained between the calculated results and the experimental data.